A source told the New York Post newspaper: "Bono kept his sunglasses on at all times. He was extremely kind to the waiters and guests."
However, the 51-year-old singer - who is renowned for his charitable work and political campaigning - did not leave empty handed, taking some chocolate goodies with him as gifts from the restaurant staff.
Bono has been seen a lot in Israel recently despite his band not playing in the country since 1997 - it is believed he is there on either business or a charity trip.
Bono - who is an avid charity and human rights campaigner - has previously joked he understands why people dislike him and his band, but he thinks that is what makes him interesting.
He said: "We're the most loved and hated band on earth. A lot of the reasons people don't like us - apart from myself, which I understand because I have to live with me too - are actually what make us interesting.
"It's the tangents, the explorations, the making mistakes in public. The audacity of thinking you can get involved in something like debt cancellation and being slagged off by your mates.
"Our diversions make us interesting."